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arXiv · 1705.03096

Partial Domination in Graphs

Benjamin M. Case·Stephen T. Hedetniemi·Renu C. Laskar·Drew J. Lipman
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Abstract

A set $S\subseteq V$ is a dominating set of $G$ if every vertex in $V - S$ is adjacent to at least one vertex in $S$. The domination number $γ(G)$ of $G$ equals the minimum cardinality of a dominating set $S$ in $G$; we say that such a set $S$ is a $γ$-set. The single greatest focus of research in domination theory is the determination of the value of $γ(G)$. By definition, all vertices must be dominated by a $γ$-set. In this paper we propose relaxing this requirement, by seeking sets of vertices that dominate a prescribed fraction of the vertices of a graph. We focus particular attention on $1/2$ domination, that is, sets of vertices that dominate at least half of the vertices of a graph $G$. Keywords: partial domination, dominating set, partial domination number, domination number

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Benjamin M. Case, Stephen T. Hedetniemi, Renu C. Laskar, Drew J. Lipman. 2017-05-08. Partial Domination in Graphs. https://arxiv.org/abs/1705.03096

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